Calculus of Variations and Geometric Measure Theory

A. Halavati

New weighted inequalities on two manifolds

created by halavati on 10 Oct 2023
modified on 23 Nov 2023



Inserted: 10 oct 2023
Last Updated: 23 nov 2023

Year: 2023

ArXiv: 2310.04868 PDF


We prove a new class of $L^2$-weighted elliptic estimates on smooth two-manifolds for positive weights $\omega$ that formally satisfy $\omega^2\Delta\ln(\omega) = -\kappa(x)\omega^2$. The proof is short and relies on a lemma about symmetric two dimensional matrices.